Help, please! My iPhone is failing to restore (code 40).

Today, I woke up to a phone call and when I hung up, my iPhone died. The screen was black and it would not respond when I held down the power button, plugged it in, etc. I took it to an AT&T store and they announced that it was an electrical issue and that the phone was simply dead. I went to my dad's house and got his old 3GS (he just got a 4S) and plugged it into my comp. It still showed as my dad's phone, even though I put my sim card into the new phone.

I looked up online how to sync my stuff to the phone and the TLDR version is this: I tried to do a factory reset in the general settings and it told me to plug my iPhone in and do a restore. I plug it in and it says "iTunes has detected an iPhone in recovery mode. You must restore this iPhone before it can be used by iTunes." It gives me an "update and restore" option, which I hit. Then it says "preparing iPhone for restore" and eventually says the iPhone is not found and gives me error code 40. I went back to AT&T and they said I'd have to take it to an Apple store. The nearest apple store? 100 miles away. I tried it on my dad's computer too, and it gave me the same error.

Does anyone have any ideas how I could fix this, short of buying a new phone?

EDIT: I should note that at no point were either iPhone jailbroken.

EDIT 2: I use Windows 7.